Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x+7y &= 5 \\ -6x-2y &= -2\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-2y = 6x-2$ Divide both sides by $-2$ to isolate $y$ $y = {-3x + 1}$ Substitute this expression for $y$ in the first equation. $3x+7({-3x + 1}) = 5$ $3x - 21x + 7 = 5$ Simplify by combining terms, then solve for $x$ $-18x + 7 = 5$ $-18x = -2$ $x = \dfrac{1}{9}$ Substitute $\dfrac{1}{9}$ for $x$ back into the top equation. $3( \dfrac{1}{9})+7y = 5$ $\dfrac{1}{3}+7y = 5$ $7y = \dfrac{14}{3}$ $y = \dfrac{2}{3}$ The solution is $\enspace x = \dfrac{1}{9}, \enspace y = \dfrac{2}{3}$.